U Kv f, @sdZddlZddlmZddlmZddlm Z ddl m Z m Z ddl m Z mZddlmZddlmZmZdd lmZd d gZd d gZd Ze eedZeeddZe eeZdDddZdEddZddZddZddZ ddZ!ddZ"ddZ#d d!Z$d d"gZ%d d#gZ&d d gZ'd d d$gZ(d d#gZ)e*d%e$fd&e#fd'e"fd(e"fgZ+d%e&e'ffd&e&e(ffd'e%e'ffd(e%e)ffgZ,e,D]\Z-Z.e.\ZZe/d e/e-eee eedd)Z0eeedd*Z1e-dd+d,kre+e-eZ2ne+e-eeZ2e/e0dd-e/e2dd-ee0e2dee1e2e2ddqxdFd/d0Z3dGd2d3Z4dHd5d6Z5d7d8Z6d9ed9dfd:d;Z7e3Z8ee8dZ9e9:d<Z;e/e;dee8dZZ=e4e8dZ>e4e8de8d?Z@e/edde/e@dde d d"gd gd?Ze/eedd@e/e AedeBeeCe7eeeeCe7eeed=dAeCeeeJsz"acovf_explicit..r)rrange)armar+Z acovfexplrr*racovf_explicitEs r0cCs|d }|d}d|dd||d|dg}|d||||d|dtdD]}|d}|||qft|S)Nr r )rr-rarray)r.r/r&r%rho_lastrrr acovf_arma11Ms && r8cCsV|d }|d }td}d|d|d|d<| |||d<| |d<|S)Nr r1rrrzeros)r/Zb1Zb2r5rrr acovf_ma2`s    r;cCs2|d }td}d|d|d<| |d<|S)Nr rr1rr9)r/r%r5rrr acovf_ma1os    r<ggg333333?ma1ma2Zarma11ar1)r+)lagsr1r/cCstddddg}tjj||dd}t|}t|}t|D]6}||t|d|ddd|d|||<q@t||D]2}||t||||ddd|||<q|||fS)Ng@gQ|g|?5^:@goŏg?)sizeZscaler3)rr4randomnormalr:r"r-r')NsigmaZtapsvuPlrrr ar_generators  40rLr3cCsN|j|}tjj|d|d|d}tjj|||djd|}||S)zReturns the autocorrelation of signal s at all lags. Adheres to the definition r(k) = E{s(n)s*(n-k)} where E{} is the expectation operator. r1r )nr)rN)shaperZfftZifft conjugatereal)srrFSZsxxrrrautocorrs "rSvalidcCs,t|||t|t||jdS)zReturns the correlation between two ndarrays, by calling np.correlate in 'same' mode and normalizing the result by the std of the arrays and by their lengths. This results in a correlation = 1 for an auto-correlationr3)r correlateZstdrN)rr#moderrr norm_corrs rWcKs|j||f|S)a9 call signature:: acorr(x, normed=True, detrend=detrend_none, usevlines=True, maxlags=10, **kwargs) Plot the autocorrelation of *x*. If *normed* = *True*, normalize the data by the autocorrelation at 0-th lag. *x* is detrended by the *detrend* callable (default no normalization). Data are plotted as ``plot(lags, c, **kwargs)`` Return value is a tuple (*lags*, *c*, *line*) where: - *lags* are a length 2*maxlags+1 lag vector - *c* is the 2*maxlags+1 auto correlation vector - *line* is a :class:`~matplotlib.lines.Line2D` instance returned by :meth:`plot` The default *linestyle* is None and the default *marker* is ``'o'``, though these can be overridden with keyword args. The cross correlation is performed with :func:`numpy.correlate` with *mode* = 2. If *usevlines* is *True*, :meth:`~matplotlib.axes.Axes.vlines` rather than :meth:`~matplotlib.axes.Axes.plot` is used to draw vertical lines from the origin to the acorr. Otherwise, the plot style is determined by the kwargs, which are :class:`~matplotlib.lines.Line2D` properties. *maxlags* is a positive integer detailing the number of lags to show. The default value of *None* will return all :math:`2 \mathrm{len}(x) - 1` lags. The return value is a tuple (*lags*, *c*, *linecol*, *b*) where - *linecol* is the :class:`~matplotlib.collections.LineCollection` - *b* is the *x*-axis. .. seealso:: :meth:`~matplotlib.axes.Axes.plot` or :meth:`~matplotlib.axes.Axes.vlines` For documentation on valid kwargs. **Example:** :func:`~matplotlib.pyplot.xcorr` above, and :func:`~matplotlib.pyplot.acorr` below. **Example:** .. plot:: mpl_examples/pylab_examples/xcorr_demo.py )Zxcorr)selfrkwargsrrrpltacorrsZma0dictZ comparefnZcasesrdargsprintZmyacovfZmyacfZothacovfrLrSrWrZrfZarrvsZarmaZfitresZacf1Zacovf1bZacf2rZacf2mZ yule_walkerrafigurer!r"ZsubplotZaxrrrrs                    > b       *